Answer:
The probability that you lose at most 2 out of your 6 races is 0.54432.
Step-by-step explanation:
We are given that you are running a race. The probability that you win is 3/5.
There are total of 6 races.
The above situation can be represented through binomial distribution;

where, n = number of trials (samples) taken = 6 races 
             r = number of success = at most 2 lost
             p = probability of success which in our question is probability that 
                   you lose a race =  1 - (3/5) = 2/5 or 0.4
Let X = <u><em>Number of races lost </em></u>
So, X ~ Binom(n = 6, p = 0.40) 
Now, the probability that you lose at most 2 out of your 6 races is given by = P(X  2)
 2) 
 P(X  2)  =  P(X = 0) + P(X = 1) + P(X = 2)
 2)  =  P(X = 0) + P(X = 1) + P(X = 2) 
 =   
  
 =   
  
 =  <u>0.54432</u>